Difference between revisions of "2021 AMC 12A Problems/Problem 22"
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==Problem== | ==Problem== | ||
| − | + | Suppose that the roots of the polynomial <math>P(x)=x^3+ax^2+bx+c</math> are <math>\cos \frac{2\pi}7,\cos \frac{4\pi}7,</math> and <math>\cos \frac{6\pi}7</math>, where angles are in radians. What is <math>abc</math>? | |
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| + | <math>\textbf{(A) }-\frac{3}{49} \qquad \textbf{(B) }-\frac{1}{28} \qquad \textbf{(C) }\frac{^3\sqrt7}{64} \qquad \textbf{(D) }\frac{1}{32}\qquad \textbf{(E) }\frac{1}{28}</math> | ||
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==Solution== | ==Solution== | ||
| − | + | {{solution}} | |
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==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=21|num-a=23}} | {{AMC12 box|year=2021|ab=A|num-b=21|num-a=23}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 15:08, 11 February 2021
Problem
Suppose that the roots of the polynomial 
are 
and 
, where angles are in radians. What is 
?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 21 |
Followed by Problem 23 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
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